How to make textures follow a certain path?
Thanks to this answer: https://blender.stackexchange.com/a/78362/20394 from Duarte Farrajota Ramos's comment, I was able to get the effect desired.

I just followed the steps in the gif linked above, and instead of selecting one face I selected the row of faces inward of the circle to the outer of the circle, proceding to do the rest of the steps from the gif. 

It worked!